85.33.62 problem 62

Internal problem ID [22685]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 62
Date solved : Thursday, October 02, 2025 at 09:06:28 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-3 y&=x^{4} {\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x)-3*y(x) = x^4*exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-{\mathrm e}^{-x}+c_1 \right ) x^{3} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 19

ode=x*D[y[x],{x,1}]-3*y[x]==x^4*Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3 \left (-e^{-x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*exp(-x) + x*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \left (C_{1} - e^{- x}\right ) \]